Question

among 2901 Accu prints not wearing seatbelts 28 were killed among 7743 occupants wearing seatbelt 14 were killed use a 0.05 significance level to test the claim that seatbelt are effective in reducing fatalities complete parts a through C

test the claim by conatructing an appropriate confidence interval

Answer 1

Ans:

sample proportion 1(not wearing)=28/2901=0.00965

sample proportion 1(wearing)=14/7743=0.00181

pooled proportion=(28+14)/(2901+7743)=0.00395

Test statistic:

z=(0.00965-0.00181)/sqrt(0.00395*(1-0.00395)*((1/2901)+(1/7743)))

z=5.75

p-value=P(z>5.75)=0.0000

Reject the null hypothesis.There is sufficient evidence to support the claim that seat belts are effective in reducing fatalities.

95% confidence interval for difference in proportions

=(0.00965-0.00181)+/-1.96*sqrt((0.00965*(1-0.00965)/2901)+(0.00181*(1-0.00181)/7743))

=0.00784+/-0.00368

=(0.00416, 0.01153)